where \(\Vert A\Vert _2\)  is the spectral norm of \(A\) , and \(L\)  is
the Lipschitz constant of \(\nabla h\)  with respect to the Euclidean norm.
Many other first-order proximal algorithms can be viewed as
special cases of (REF ),
and their connections are summarized in Figure REF .
When \(h=0\) , algorithm (REF ) reduces to the (primal)
primal–dual hybrid gradient (PDHG) method [1]}, [2]}, [3]},
or PDHGMu in [4]}.
When \(g=0\)  in (REF ) (and assuming \(z^{(0)}=0\) ),
we obtain the proximal gradient algorithm.
When \(f=0\) , we obtain a variant of the Loris–Verhoeven algorithm
[5]}, [6]}, [7]},
\(x^{(k+1)} &= x^{(k)}-\tau (A^Tz^{(k)}+\nabla h(x^{(k)})) \\z^{(k+1)} &= \mathrm {prox}_{\sigma g^\ast }\big ((I-\sigma \tau AA^T) z^{(k)}+\sigma A(x^{(k+1)}-\tau \nabla h(x^{(k)}) \big ).\) 
